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STABILITY OF THE SOLAR SYSTEM. 323 
duction, the reader will have no difficulty in admitting 
that the word elegance may be appropriately applied to 
mathematical researches. 
In this analysis we have merely glanced at the astro- 
nomical discoveries of Clairaut, D’Alembert, and La- 
grange. We shall be somewhat less concise in noticing 
the labours of Laplace. 
After having enumerated the various forces which must 
result from the mutual action of the planets and satellites 
of our system, even the great Newton did not venture to 
investigate the general nature of the effects produced by 
them. In the midst of the labyrinth formed by increases 
and diminutions of velocity, variations in the forms of the 
orbits, changes of distances and inclinations, which these 
forces must evidently produce, the most learned geometer 
would fail to discover a trustworthy guide. This extreme 
complication gave birth to a discouraging reflection. 
Forces so numerous, so variable in position, so different 
in intensity, seemed to be incapable of maintaining a con- 
dition of equilibrium except by a sort of miracle. New- 
ton even went so far as to suppose that the planetary 
system did not contain within itself the elements of indef- 
inite stability; he was of opinion that a powerful hand 
must intervene from time to time, to repair the derange- 
ments occasioned by the mutual action of the various 
bodies. Euler, although farther advanced than Newton 
in a knowledge of the planetary pertubations, refused 
also to admit that the solar system was constituted so as 
to endure for ever. 
Never did a greater philosophical question offer itself 
to the inquiries of mankind. Laplace attacked it with 
boldness, perseverance, and success. ‘The profound and 
long-continued researches of the illustrious geometer 
